3) Consider a 10-year coupon bond and a 30-year coupon bond, both with 10% annual coupons. These two bonds pay semiannual coupon payments based on the face value of $100. (a) By what percentage (%) will the price of each bond change if its yield to maturity (YTM) increases from 7% to 8% ? (10\%) (b) Explain the relationship between the maturity and interest rate changes (risk). (5\%) 4) Suppose you purchase a 20-year, zero-coupon bond with a yield to maturity (YTM) of 5% and the face value is $1000. (15\%) (a) What would the initial price be? (b) If the bond's yield to maturity remains at 5%, what will its price be five years later? (c) If you purchased the bond at the above initial price and sold it five years later, what would the rate of return of your investment be